# An integral formula for Riemannian $G$-structures with applications to almost Hermitian and almost contact structures

## TL;DR

This paper derives an integral formula for Riemannian G-structures by computing the divergence of a vector field related to intrinsic torsion, with applications to almost Hermitian and almost contact structures.

## Contribution

It introduces a new integral formula for Riemannian G-structures and interprets it in specific cases like almost Hermitian and contact structures.

## Key findings

- Derived divergence formula for intrinsic torsion vector field
- Established integral formula on closed Riemannian manifolds
- Applied results to almost Hermitian and contact structures

## Abstract

For a Riemannian $G$-structure, we compute the divergence of the vector field induced by the intrinsic torsion. Applying the Stokes theorem, we obtain the integral formula on a closed oriented Riemannian manifold, which we interpret in certain cases. We focus on almost harmitian and almost contact metric structures.